\newproblem{lay:5_4_27}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 5.4.27}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $V$ be $\mathbb{R}^n$ with a basis $\mathcal{B}=\{\mathbf{b}_1,\mathbf{b}_2,...,\mathbf{b}_n\}$; let $W$ be $\mathbb{R}^n$ with the standard basis,
	denoted here by $\mathcal{E}$; and consider the identity transformation $I: V \rightarrow W$, $I(\mathbf{x})=\mathbf{x}$. Find the matrix for $I$ relative 
	to $\mathcal{B}$ and $\mathcal{E}$. What was this matrix called in the context of coordinate systems (Section 4.4)?
}{
  % Solution
	The transformation matrix is given by
	\begin{center}
		$\begin{array}{rcl}M&=&\begin{pmatrix} [I(\mathbf{b}_1)]_{\mathcal{E}} & [I(\mathbf{b}_2)]_{\mathcal{E}} & ... & [I(\mathbf{b}_n)]_{\mathcal{E}} \end{pmatrix}\\
		   &=&\begin{pmatrix} \mathbf{b}_1 & \mathbf{b}_2 & ... &\mathbf{b}_n\end{pmatrix}
		\end{array}$
	\end{center}
	This was the change of coordinates matrix in Section 4.4, denoted as $P_{\mathcal{E}\leftarrow \mathcal{B}}$.
}
\useproblem{lay:5_4_27}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
